Image rectification is a transformation process used to project two-or-more images onto a common image plane. It corrects image distortion by transforming the image into a standard coordinate system.
- It is used in computer stereo vision to simplify the problem of finding matching points between images.
- It is used in geographic information systems to merge images taken from multiple perspectives into a common map coordinate system.
Computer stereo vision
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Between two cameras there is a problem[clarification needed] of finding a corresponding point viewed by one camera in the image of the other camera (known as the correspondence problem). In most camera configurations, finding correspondences requires a search in two-dimensions. However, if the two cameras are aligned to be coplanar, the search is simplified to one dimension - a horizontal line parallel to the line between the cameras. Furthermore, if the location of a point in the left image is known, it can be searched for in the right image by searching left of this location along the line, and vice versa (see binocular disparity). Image rectification is an equivalent (and more often used) alternative to perfect camera alignment. Image rectification is usually performed regardless of camera precision[clarification needed], because it may be impractical to perfectly align cameras, and even perfectly aligned cameras may become misaligned over time.
If the images to be rectified are taken from camera pairs without geometric distortion, this calculation can easily be made with a linear transformation. X & Y rotation puts the images on the same plane, scaling makes the image frames be the same size and Z rotation & skew adjustments make the image pixel rows directly line up. The rigid alignment of the cameras needs to be known (by calibration) and the calibration coefficients are used by the transform.
In performing the transform, if the cameras themselves are calibrated for internal parameters, an essential matrix provides the relationship between the cameras. The more general case (without camera calibration) is represented by the fundamental matrix. If the fundamental matrix is not known, it is necessary to find preliminary point correspondences between stereo images to facilitate its extraction.
Geographic information system
Image rectification in GIS converts images to a standard map coordinate system. This is done by matching ground control points (GCP) in the mapping system to points in the image. These GCPs calculate necessary image transforms.
Primary difficulties in the process occur
- when the accuracy of the map points are not well known
- when the images lack clearly identifiable points to correspond to the maps.
The maps that are used with rectified images are non-topographical. However, the images to be used may contain distortion from terrain. Image orthorectification additionally removes these effects.
Image rectification is a standard feature available with GIS software packages.
- Binocular disparity
- Correspondence problem
- Epipolar geometry
- Geographic information system
- Stereo camera
- Stereo vision
- Structure from motion
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- Computing Rectifying Homographies for Stereo Vision by Charles Loop and Zhengyou Zhang (April 8, 1999) Microsoft Research